TITLE:
Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue
AUTHORS:
Shouzhong Fu, Zhong Wang
KEYWORDS:
Differential Operators, Eigenvalue, Algebraic Multiplicities, Geometric Multiplicities, Analytic Multiplicities
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.15,
August
5,
2014
ABSTRACT: In this paper, the algebraic, geometric and analytic multiplicities of
an eigenvalue for linear differential operators are defined and classified. The
relationships among three multiplicities of an eigenvalue of the linear
differential operator are given, and a fundamental fact that the algebraic,
geometric and analytic multiplicities for any eigenvalue of self-adjoint
differential operators are equal is proven.